Question

complete the proof.
given: $overline{km}congoverline{nm}$, $overline{lk}congoverline{ln}$
prove: $\triangle lkmcong\triangle lnm$
statements reasons
$overline{km}congoverline{nm}$ x
$overline{lk}congoverline{ln}$ y
$overline{lm}congoverline{lm}$ z
$\triangle klmcong\triangle lnk$ a

Explanation:

Step1: Identify first given

The statement $\overline{KM}\cong\overline{NM}$ is given in the problem setup.

Step2: Identify second given

The statement $\overline{LK}\cong\overline{LN}$ is given in the problem setup.

Step3: Understand reflexive property

$\overline{LM}\cong\overline{LM}$ because any segment is congruent to itself (reflexive property).

Step4: Apply congruence postulate

Since we have three pairs of congruent sides ($\overline{KM}\cong\overline{NM}$, $\overline{LK}\cong\overline{LN}$, $\overline{LM}\cong\overline{LM}$), by the SSS congruence postulate, $\triangle KLM\cong\triangle LNK$.

Answer:

[x] Given
[y] Given
[z] Reflexive Property of Congruence
[a] SSS (Side - Side - Side) Congruence Postulate